In the semiconductor industry, microlithography (or simply lithography) is the process of printing circuit patterns on a semiconductor wafer (for example, a silicon or GaAs wafer). Currently, optical lithography is the predominant technology used in volume manufacturing of semiconductor devices and other devices such as flat-panel displays. Such lithography employs light in the visible to deep ultraviolet spectrum range to expose photo-sensitive resist on a substrate. In the future, extreme ultraviolet (EUV) and soft x-rays may be employed. Following exposure, the resist is developed to yield a relief image.
In optical lithography, a photomask (often called a mask or a reticle) that serves as a template for the device structures to be manufactured is first written using electron-beam or laser-beam direct-write tools. A typical photomask for optical lithography consists of a glass (or quartz) plate of six to eight inches on a side, with one surface coated with a thin metal layer (for example, chrome) of a thickness of about 100 nm. The device pattern is etched into the metal layer, hence allowing light to transmit through the clear areas. The areas where the metal layer is not etched away block light transmission. In this way, a pattern may be projected onto a semiconductor wafer.
The mask contains certain patterns and features that are used to create desired circuit patterns on a wafer. The tool used in projecting the mask image onto the wafer is called a “stepper” or “scanner” (hereinafter collectively called “exposure tool”). FIG. 1 is a diagram of an optical projection lithographic system 10 of a conventional exposure tool. System 10 includes an illumination source 12, an illumination pupil filter 14, a lens subsystem 16a-c, a mask 18, a projection pupil filter 20, and a wafer 22 on which the aerial image of mask 18 is projected. Illumination source 12 may be laser source operated, for example, at UV (ultra-violet) or DUV (deep ultra-violet) wavelengths. The light beam of illumination source 12 is expanded and scrambled before it is incident on illumination pupil 14. Illumination pupil 14 may be a simple round aperture, or may have specifically designed shapes for off-axis illumination. Off-axis illumination may include, for example, annular illumination (i.e., illumination pupil 14 is a ring with a designed inner and outer radius), quadruple illumination (i.e., illumination pupil 14 has four openings in the four quadrants of the pupil plane), and other shapes like dipole illumination.
After illumination pupil 14, the light passes through the illumination optics (for example, lens subsystem 16a) and is incident on mask 18, which contains the circuit pattern to be imaged on wafer 22 by the projection optics. As the desired pattern size on wafer 22 becomes smaller and smaller, and the features of the pattern become closer and closer to each other, the lithography process becomes more challenging. In an effort to improve imaging quality, current processing techniques employ resolution enhancement techniques (“RET”), such as, for example, optical proximity correction (“OPC”), phase shift masks (“PSM”), off-axis illumination (“OAI”), and condenser and exit pupil filters. Many of the RET technologies are applied on or directly to mask 18. For example, OPC and PSM, which modify the light waves to compensate for the imperfection of the imaging properties of the projection optics (for example, the OPC technology is used to compensate for optical or processing related proximity effects, e.g., due to light interference), and/or take advantage of designed light interferences to enhance the imaging quality, for example, the PSM technology is used to create phase shifting between neighboring patterns to enhance resolution. Notably, mask 18 may not be “perfect,” due to its own manufacturing process. For example, corners on mask 18 may not be sharp but may be rounded and/or the linewidth may have a bias from design value where the bias may also depend on the designed linewidth value and neighboring patterns. These imperfections on mask 18 may affect the final imaging quality.
The projection optics (for example, lens subsystems 16b and 16c, and projection pupil filter 20) images mask 18 onto wafer 22. Pupil 20 of the projection optics limits the maximum spatial frequency of the mask pattern that can be passed through the projection optics system. A number called “numerical aperture” or NA often characterizes pupil 20. There are also proposed RET techniques that modify pupil 20, which are generally called pupil filtering. Pupil filtering may include modulating both the amplitude and the phase of the light beams passing through pupil 20.
Due to the wavelength of light being finite, and current techniques employing wavelengths that are larger than the minimum linewidth that is printed on wafer 22, there are typically significant light interference and diffraction effects affecting the imaging process. The imaging process does not produce at the wafer plane a perfect replication of the pattern on mask 18. In order to predict the actual imaging performance, current techniques employ physical theory to simulate and model this imaging process. Further, due to the high NA value of current lithography tools, different polarizations of the light provide different imaging properties. To more accurately model the imaging process, a vector-based model may be used that incorporates polarization effects.
The projection optics of system 10 may be diffraction-limited. However, lens subsystem 16b and 16c in the projection optics are most often not completely “perfect.” These imperfections may be due to aberrations, which are often modeled as some undesired phase modulation at the plane of pupil 20, and are commonly represented by a set of Zernike coefficients. After the light finally reaches the surface of wafer 22, it will further interact with the coatings on wafer 22 (for example, the photoresist). In this regard, different resist thickness, different optical properties of the resist (for example, its refractive index), and different material layers under the resist (for example, a bottom-anti-reflection-coating or BARC), may further affect the imaging characteristics. Some of these effects may also be abstracted by a modulation at the pupil plane.
When the resist is exposed by the projected image and thereafter baked and developed, the resist tends to undergo complex chemical and physical changes. The final resist patterns are typically characterized by their critical dimensions, or CD, usually defined as the width of a resist feature at the resist-substrate interface. While the CD is usually intended to represent the smallest feature being patterned in the given device, in practice the term CD is used to describe the linewidth of any resist feature.
For a lithography process to pattern a device correctly, the CDs of all critical structures in the device must be patterned to achieve the design target dimensions. Since it is practically impossible to achieve every target CD with no errors, the device is designed with a certain tolerance for CD errors. In this case, the pattern is considered to be acceptable if the CDs of all critical features are within these predefined tolerances. In order for the lithography process to be viable in a manufacturing environment, the full CD distribution must fall within the tolerance limits across a range of process conditions, which represents the typical range of process variation expected to occur in the fab.
The range of process conditions over which the CD distribution will meet the specification limits is referred to as the “process window.” While many variables must be considered to define the full process window, in lithography processes it is typical to describe only the two most critical process parameters, focus and exposure offsets, in defining the process window. A process may be considered to have a manufacturable process window if the CDs fall within the tolerance limits, e.g., +/−10% of the nominal feature dimension, over a range of focus and exposure conditions which are expected to be maintainable in production. FIG. 2 is a diagram of a process window 30 as an area in exposure-defocus (E-D) space in which CDs are within tolerance limits for up to +/−150 nm of focus error and +/−15% exposure error. It should be noted that while this may seem to be an unusually large range of exposure variation, given that state of the art exposure tools can easily control the energy delivered at the wafer plane to less than 1% variation, the exposure dose tolerance must be significantly larger than the expected variation in energy since exposure latitude also serves as a surrogate for a wide range of other process variations such as film thickness, reflectivity, resist processing, develop processing, exposure tool aberrations, and others. It should also be noted that different pattern types or sizes usually have different process windows, and that the manufacturability of a device design depends on the common process window of all critical patterns.
First-principle and empirical models have been developed to simulate lithography processes, including the formation of the aerial image (the image projected onto wafer 22), transfer of the aerial image into a latent image in the resist film, and baking and developing of the resist to form the final three-dimensional resist pattern. These models are vital in verifying that the complex circuit patterns, including RET enhancements, will be reproduced correctly and with a manufacturable process window at the wafer level. The time and expense needed to create test masks, expose them, process test wafers and determine the final dimensions experimentally would be prohibitive without the savings in time and processing cost made possible by simulation. Simulation can also be used to study the patterning of the full chip image and predict any weak spots in the design, for example by a process window analysis (see U.S. Pat. No. 7,003,758, the subject matter of which is hereby incorporated by reference in its entirety), to develop the OPC and PSM models used in developing and implementing the RETs used to create the mask pattern, and to develop model-based advanced process control systems used to monitor and control the lithography process in production (see “Lithography Process Control,” H. J. Levinson, Solid State Technology, Vol. 40, No. 11, pp. 141-149 (November 1997); “Semiconductor Process Control,” L. Mantalas and H. Levinson, Handbook of Critical Dimension Metrology and Process Control, K. Monahan, editor, SPIE Critical Review of Optical Science and Technology, Vol. CR52, pp. 230-266 (1994)).
In developing and calibrating the models used for all aspects of lithography simulation, one of the most difficult challenges has been the correct separation of the model into its optical and resist components, where the optical model module accurately represents the formation of the aerial image by the exposure tool and the resist model module accurately represents the absorption of the incident aerial image by the resist as well as the development of the exposed resist to form the final three-dimensional resist pattern. A model of a lithography process includes an optical model module, and may optionally include a resist model module, a mask model module, and other appropriate model modules. The model modules of the model of the lithography process will be referred to herein as models, e.g., the optical model and the resist model, for simplicity.
Up until now, the only way to calibrate a lithography simulation model has been to process a wafer in an exposure tool, develop the resist images, measure the CDs and possibly sidewall angles of the resist profile, then adjust both optical and resist model parameter values to achieve the best possible agreement between predicted and measured resist observations. FIG. 3 is a flowchart of a prior art method used to process wafers in an exposure tool and collect data using any current CD metrology tool such as a CD Scanning Electron Microscope (CD-SEM), scatterometer (SCD), optical CD (OCD), electrical linewidth (ELM) or Atomic Force Microscopy (AFM) tool. FIG. 4 is a flowchart of a prior art method for calibrating a model of a lithography process, where simulated resist data (CDs, sidewall angles, contours and/or three-dimensional profiles) are compared to measured resist data in step 420 to evaluate the model quality and any differences between the modeled and the measured results are used to modify both the optical and resist models in step 424. In the method of FIG. 4, the model only includes an optical model and a resist model for ease of illustration. Assuming that the measured data are sufficiently accurate, any differences between the model predictions for the resist patterns and the measurements of the actual resist patterns could be due to inaccuracy in either the resist model or the optical model.
There is presently no unambiguous method to separate which model component needs to be adjusted in order to reduce such differences, and thereby to improve the predictability of the simulation model. Consequently, often a resist parameter may be changed to compensate for an incorrect setting of an optical parameter, or vice versa. Selection of a non-optimal parameter set often results in incomplete convergence of the model fitting procedure, or, if the model fitting does converge, the values to which the parameters converge often have little relationship to physical reality and therefore provide limited predictability.
In this current environment, the model prediction may be optimized for a restricted set of calibration test patterns, but the terms in the model may not be correct, leading to incorrect predictions of patterns that were not included in the set of calibration test patterns. In addition, if a model is calibrated without achieving a significant match between model parameters and real physical parameters, model predictability will be limited in the following respect: if one specific parameter is deliberately changed in the process, such as the partial coherence (sigma) of the illuminator or the numerical aperture (NA) of the projection lens, simply changing that parameter in the model will most likely not give the correct results. A change in one known parameter may require corresponding changes in multiple modeling terms to restore the model accuracy. In effect, the model terms, although they are given names corresponding to real physical parameters, do not actually represent those specific parameters but rather they represent the collective effect of numerous different parameters convolved into empirical modeling terms.
In many cases, developers of lithography simulation models have recognized the difficulty in developing truly separable models and have tacitly admitted that the model parameters do not bear a unique one-to-one correspondence with the physical parameters for which they are named. In such “lumped parameter” models, the model terms are given physical sounding names, but the values which these parameters are set to, in order to achieve the best matching to experimental data, do not actually correspond to the physical value those parameters would have if they could be individually measured in the process. (See “Lumped Parameter Model for Optical Lithography,” R. Hershel and C. Mack, Ch. 2, Lithography for VLSI, VLSI Electronics—Microstructure Science, R. K. Watts and N. G. Einspruch, eds., Academic Press (New York), pp. 19-55 (1987); “Enhanced Lumped Parameter Model for Photolithography,” C. A. Mack, Optical/Laser Microlithography VII, Proc. SPIE Vol. 2197, pp. 501-510 (1994); “3D Lumped Parameter Model for Lithographic Simulation,” J. Byers., M. D. Smith, C. A. Mack, Optical/Laser Microlithography XV, A. Yen, editor, Proc. SPIE Vol. 4691, pp. 125-137 (2002)). As a result, if any term in the real physical process is deliberately changed, it is not sufficient to change the one corresponding term in the model. Instead, the entire model must be recalibrated. In many cases, even if the process change is only in the optical parameters, all of the resist parameters in the model may also require returning, and vice versa: if the change is only in the resist parameters, the optical model might also need to be returned. Thus, if an optical parameter such as NA or sigma is changed, the optical and resist models both need to be returned. This indicates that such models and the methods used to calibrate the models do not achieve true, physically significant model separation. As a result, any change in the process requires extensive, time consuming model recalibration.
Other models have been developed which take the lack of separability to such an extreme that they do not even attempt to break the model into separate optical and resist components. Examples of such models are the class of lumped parameter or behavioral models often used in OPC implementation. The use of non-separable models means that an OPC model that is optimized for a given exposure tool and a given resist process is not easily transferable to another tool or another resist process. Due to the convoluted mapping of real physical parameters with these OPC model parameters, an entirely new model would have to be developed even if process changes seem relatively minor.
Some efforts have been made to develop first-principle resist models (see “New Kinetic Model for Resist Dissolution,” C. A. Mack, Jour. Electrochemical Society, Vol. 139, No. 4, pp. L35-L37, April 1992) and to measure the resist parameters independently through specific tests, such as dose-to-clear, contrast curves, and development rate monitors (see “Characterization of Positive Photoresist,” F. H. Dill et al., IEEE Trans. Electronic Devices, ED-22, No. 7, pp. 445-452, July 1975). The goal of such first-principle approaches is to provide truly separable models such that the terms in the models do bear a unique one-to-one correspondence with the physical parameters of interest. Efforts to implement workable first-principle models have been largely unsuccessful due to a number of factors: the large number of resist parameters required to accurately describe the complex kinetics of acid and base diffusion in modern acid catalyzed resist systems as well as the surface and substrate interaction effects in these resists; the sensitivity to the various bake temperatures and thermal cycles; the difficulty in accurately modeling the development path at the developer-resist interface, where the resist film undergoes a complex phase transformation from solid to soluble gel; and the molecular level perturbations of the acid and base species in the resist which gives rise to stochastic line edge roughness (see “Resist Blur and Line Edge Roughness,” G. Gallatin, Optical Microlithography XVIII, B. W. Smith, editor, Proc. SPIE, Vol. 5754, pp. 38-52 (2005)).
Even if a microscopic resist model could be simplified from the physical reality to a manageable set of parameters, the linkage between the resist model and optical model is still difficult to break due to the lack of understanding of the exact optical conditions in the exposure tool. While it is common to represent the illumination profile by a simple set of parameters, such as the single parameter sigma for conventional illumination or the two parameters inner and outer sigma for annular illumination, the actual pupil fill function is far more complex and non-uniform, both spatially in the mask plane and in terms of the pupil filling factor in the conjugate plane (see “Size-Dependent Flare and its Effect on Imaging,” Stephen Renwick et al., Optical Microlithography XVI, A. Yen, editor, Proc. SPIE Vol. 5040, pp. 24-32 (2003)). Similarly, the wavefront will be significantly aberrated from its idealized representation by lower order terms, often represented as Zernike polynomials (see “Zernike Coefficients: Are They Really Enough?,” C. Progler and A. Wong, Proc. SPIE, Vol. 4000, pp. 40-52 (2000); “Analysis of Imaging Performance Degradation,” K. Matsumoto, Optical Microlithography XVI, A. Yen, editor, Proc. SPIE, Vol. 5040, pp. 131-138 (2003)), as well as mid-to-low spatial frequency terms such as flare (see “Analysis of Flare and its Impact on Low-k1 KrF and ArF Lithography,” Bruno La Fontaine et al., Optical Microlithography XV, A. Yen, editor, Proc. SPIE, Vol. 4691, pp. 44-56 (2002); “Measuring and Modeling Flare in Optical Lithography,” Chris Mack, Optical Microlithography XVI, A. Yen, editor, Proc. SPIE, Vol. 5040, pp. 151-161 (2003); “Flare and its Effects on Imaging,” Stephen P. Renwick, Optical Microlithography XVII, B. W. Smith, editor, Proc. SPIE, Vol. 5377, pp. 442-450 (2004); “Scattered Light: The Increasing Problem for 193 nm Exposure Tools and Beyond,” K. Lai, C. Wu, and C. Progler, Optical Microlithography XIV, C. Prolger, editor, Proc. SPIE, Vol. 4346, pp. 1424-1435 (2001)). These deviations from idealized theory can cause extensive proximity effects which are difficult to separate from resist processing effects.